Quantative problem solving - Essay Example

On the other hand, Carol recommends the Exer-Trim program of the XYZ Fitness Club which offers a daily pass and use of gym and other health facilities worth $2.56 inclusive of supplements at a fixed annual cost of $307. As a challenge to herself, Tanya has to decide on the option that would enable her to lose weight and save money on the first 60 days prior to their out-of-the-country vacation. A. Analyze the cost of each option algebraically – Each cost equation may be written in the slope-intercept form y = mx + b, Assuming that the value of the daily set meal under the U-Light program is not subject to change, then Tanya would have to pay a constant rate of $5.

13 if she chooses to diet without workout and agree to cover the $145-annual fee. Hence, the cost of enrolment for the U-Light package may be set, depending on the number of days (t) signed up for, as: C(t) = 5.13*t + 145 (in which the slope (m) is the rate $5.13 charge per day and the y-intercept (b) assumes the fixed cost of $145 (on a yearly basis)). Considering the Exer-Trim program, nevertheless, Tanya has the alternative of visiting the XYZ club for an extensive workout that can make her thoroughly fit even in the absence of restricting diet on food.

She just needs to pay a uniform daily rate of $2.56 that comes with fixed settlement of $307 for supplementary items such that, depending also on the number of days (t) enrolled for, it would cost her: C(t) = 2.56*t + 307 (in which the slope (m) is the rate $2.56 charge per day and the y-intercept (b) is given by the fixed cost of $307 (on a yearly basis)) C(t) stands for ‘cost in dollars’ whereas ‘t’ represents the number of days (diet and exercise) and to find solution where the values of C(t) and t are the same for both schemes, equate 5.

13*t + 145 = 2.56*t + 307 which becomes 2.57*t = 162 (on combining like terms) ---? t ? 63.035 days (upon division of each side by 2.57) Then, substituting this value of ‘t’ into one of the original equations: C(63.035) = 5.13*(63.035) + 145 ---? C(63.035) ? $468.37 This means that the solution is approximately at: B. Depict the real-world problem on a single graph – Sketch of the Graph: Total Workout or Diet Meal Cost (per package) C(t) t-days (diet or exercise) C. Discuss a decision-making process that is based on both mathematical reasoning and non-financial, or situational, considerations.

After solving the system of equations and sketching each linear graph on the xy-plane, Tanya can now decide according to the following outcomes: At t > 63.035 days, it would cost Tanya too much to go on a south beach diet with U-Light program whereas at t < 63.035 days, it is rather expensive to go after extensive workout with Exer-Trim program. Since Tanya’s priority is to save money for the first 60 days of her weight loss scheme, she must then opt for the U-Light program and go on south beach diet that merely includes one pass to the gym.

The graph shows that she can save more for the Bali-getaway if she agrees to pay $5.13 a day for a south beach diet meal with fixed annual service charge of $145. In that case, she would